Question: Simplify the following expression: $ q = \dfrac{9r - 9}{10r} - \dfrac{-1}{6} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6}{6}$ $ \dfrac{9r - 9}{10r} \times \dfrac{6}{6} = \dfrac{54r - 54}{60r} $ Multiply the second expression by $\dfrac{10r}{10r}$ $ \dfrac{-1}{6} \times \dfrac{10r}{10r} = \dfrac{-10r}{60r} $ Therefore $ q = \dfrac{54r - 54}{60r} - \dfrac{-10r}{60r} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{54r - 54 + 10r }{60r} $ Distribute the negative sign: $q = \dfrac{54r - 54 + 10r}{60r}$ $q = \dfrac{64r - 54}{60r}$ Simplify the expression by dividing the numerator and denominator by 2: $q = \dfrac{32r - 27}{30r}$